Here, \(n_{x}\)  and \(n_{y}\)  are the sides
of a rectangular simulation domain, and \(\gamma =1\) . Eq. REF 
follows from the numerical scheme introduced by Melenthin et al. [1]}
that allows equilibrium states to be attained faster in comparison
to the standard equation of motion of the PFC model [2]}.
Here, \(\psi \) , is treated as a locally nonconserved order parameter,
while the mass conservation, \(\int \psi d\vec{x}\) , is ensured globally.
Other approaches to model faster dynamics for the peak density field
can be found in the work by Heinonen et al. [3]}.
Note, the variational derivative in Eq. REF  introduces coupled
composition-lattice symmetry terms. These coupled terms affect the
symmetry of the periodic system. 
